Tree squirrels and ground squirrels occasionally require population control measures, around here. But, they carry the plague in most areas. So, they're magpie and hawk food. (Or bait for more squirrels -- they're cannibalistic.)

My preferred platform is a Marlin 882 in .22 WMR.
.22 LR works; but .22 WMR is more accurate, flatter-shooting, and much more effective.